Does PNG files size affect video output file size?
Yes...and no.

First of all, I would 100% recommend that you render at the same resolution that you plan to make your video unless you're planning on using AI Upscaling. Doing otherwise would result in the same effect that zooming really closely into an image produces - you start seeing the individual pixels.

Video files will always be smaller than the summation of the frame outputs. That's because videos don't actually store every single frame as an image, they instead use algorithms to store some frames and record what changes between different frames. Rather than trying to explain this myself here's a good short video explanation for this by Tom Scott on Youtube.

From my experience (and it should be noted that I've done some video editing using Adobe Premiere in the past, but nothing professionally), you shouldn't need to further compress the video - MPG4 will already compress the output to be much much smaller.